It comes days before a Budget in which Rachel Reeves is expected to launch a raid on property wealth and weeks after Angela Rayner was sacked over stamp duty scandal.

Mr Healey blamed his underpayment on “an administrative error” by Westminster City Council.

Following the introduction of the second home council tax surcharge in April, the Cabinet minister is supposed to pay £2,938 in tax to Westminster City council annually for the flat, which he is understood to use for work.

But it has emerged he paid only half as much for this tax year, and rectified the mistake on Thursday only after being approached by it.

A spokesman for the Defence Secretary blamed the underpayment on the local authority, saying “an administrative error” meant it had failed to classify his home correctly for council tax purposes, leading “to an incorrect council tax notice being issued”.

They insisted Mr Healey had “fulfilled all his obligations as a tenant by notifying Westminster council of the second home status of the tenancy on the council tax registration form when the tenancy began”, adding that he had now paid all tax in full.

But the Tories said there were still questions to answer about why he had failed to notify the council of the underpayment when he received the “incorrect” bill.

Mr Healey is the latest Cabinet minister to have been caught mishandling their personal affairs. Ms Reeves was forced to admit that she had broken rules for landlords when letting out her south London home without a licence last month. She blamed the oversight on her letting agents.

Angela Rayner, the former deputy prime minister, resigned in September after The Telegraph revealed that she had failed to pay a £40,000 stamp duty bill on the purchase of a flat in Hove.

Rushanara Ali, the UK’s former minister for homelessness, stepped down in August after she was accused of evicting her tenants and then re-listing the property at a higher rent. In her resignation letter, she said she had followed “all relevant legal requirements,” but said she had become a distraction for the Government.

Kevin Hollinrake, the chairman of the Conservative Party, said: “Whether it’s the anti-corruption minister being investigated for corruption, the homelessness minister who evicted her own tenants, or the housing secretary who failed to pay her stamp duty, with this Government it is one rule for them and another for everyone else.

“Healey needs to come clean about what he knew and when. If we cannot trust senior ministers to keep their own tax affairs in order, how can we trust them to run the country?”

Laila Cunningham, of Reform UK, said: “As a Westminster councillor, I see residents chased for far smaller sums. Yet a Cabinet minister underpays thousands and only fixes it when journalists ring. It’s the same old story, the people in charge don’t live under the rules they impose on everyone else.”

Mr Healey owns his main home in his constituency of Rawmarsh and Conisbrough, where he lives with his wife, and began letting a Westminster flat last November.

A spokesman for Mr Healey told the Telegraph, who uncovered details of the underpayment: “The Secretary of State fulfilled all his obligations as a tenant by notifying Westminster council of the second home status of the tenancy on the council tax registration form when the tenancy began.

“Westminster council made an administrative error which failed to classify it as a second home for council tax purposes, and led to an incorrect council tax notice being issued. The council have accepted fault and apologised for the error.

“Westminster council have rectified this mistake and the council tax liability, including the second homes surcharge, on the London flat has been paid in full.”

A council spokesman said: “The Secretary of State filled in the form correctly and registered the address as a second home. There was an oversight by the council, and we did not register it as a second home. This led to an incorrect council tax notice being issued. We apologise for the error.”